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Using (x+a)(x+b)=x2+(a+b)x+ab, find
(i) 103 x 104
(ii) 5.1 x 5.2
(iii) 103 x 98
(iv) 9.7 x 9.8
Answer :

i) 103 x 104
= (100 + 3)(100 + 4)
=1002+(3+4)100+12
= 10000 + 700 + 12 = 10712
ii) 5.1 x 5.2
= (5 + 0.1)(5 + 0.2)
= 52 + (0.1 + 0.2)5 + 0.1 x 0.2
= 25 + 1.5 + 0.02 = 26.52
iii) 103 x 98
= (100 + 3)(100 – 2)
= 1002+ (3-2)100 – 6
= 10000 + 100 – 6
= 10094
iv) 9.7 x 9.8
= (9 + 0.7 )(9 + 0.8)
= 92+ (0.7 + 0.8)9 + 0.56
= 81 + 13.5 + 0.56
= 95.06